About the Implicit Differentiation Calculator
Some curves, like circles x² + y² = r² or the folium x³ + y³ = 6xy, cannot easily be written as y = f(x). Implicit differentiation finds their slope anyway: differentiate both sides with respect to x, remembering that y depends on x, so every y-term picks up a factor dy/dx by the chain rule.
The calculator moves everything to one side, F(x, y) = 0, and uses dy/dx = −F_x/F_y, where F_x and F_y are partial derivatives. It simplifies the answer, gives the slope and tangent line at a point on the curve, and the second derivative d²y/dx².